Nonholonomic Dynamics and Integrability (07w5029)

Arriving in Banff, Alberta Sunday, January 28 and departing Friday February 2, 2007


Boris Khesin (University of Toronto)

(Pennsylvania State University)


Nonholonomic mechanics describes the motion of systems subbordinated to non-holonomic constraints, i.e. systems whose restrictions on velocities do not arise from the constraints on the configuration space. The best known examples of such systems are a sliding skate and a rolling ball, as well as their numerous generalizations. These systems usually exhibit very peculiar, often counter-intuitive, behavior. For example, a golf ball rolls while oscillating inside a vertical tube, seemingly defying gravity, and a rattleback top (Celtic stone) spins only in one direction and resists spinning in the opposite one. Non-holonomic mechanics is also a cornerstone of the control theory, where the non-holonomic property is pivotal in the descriptions of attainable configurations.

The integrability vs. chaos of such systems is one of their main points of interest, which is yet to be better understood. There are competing paradigms in the corresponding theories: the variational and non-variational ones. A more profound understanding of their relation to each other, the applications of them to control theory, as well as the similarities with Hamiltonian systems would be very important for the further progress in the theory. Such domains as sub-Riemannian geometry, Hamiltonian systems, billiard theory (in particular, billiards in magnetic field), sub-elliptic operators, motion planning in robotics have recently manifested new interesting features close to non-holonomic systems phenomena. This workshop is an opportunity to bring specialists in these domains together and foster interactions between researchers with diverse and often complimentary backgrounds in the domain of non-holonomic mechanics and in the adjacent areas.